Reduction of m-Regular Noncrossing Partitions [article]

William Y. C. Chen, Eva Y. P. Deng, Rosena R. X. Du
2004 arXiv   pre-print
In this paper, we present a reduction algorithm which transforms m-regular partitions of [n]={1, 2, ..., n} to (m-1)-regular partitions of [n-1]. We show that this algorithm preserves the noncrossing property. This yields a simple explanation of an identity due to Simion-Ullman and Klazar in connection with enumeration problems on noncrossing partitions and RNA secondary structures. For ordinary noncrossing partitions, the reduction algorithm leads to a representation of noncrossing partitions
more » ... n terms of independent arcs and loops, as well as an identity of Simion and Ullman which expresses the Narayana numbers in terms of the Catalan numbers.
arXiv:math/0406180v1 fatcat:s4ervrokkzgxziein7q4uglgki